Piezoelectric crystal element



Oct. 4, 1949. H, JAFFE 2,483,641

PIEZOELECTRIC CRYSTAL ELEMENT Filed Feb. 16, 1948 2 Sheets-Sheet lINVENTOR. HANS. JAFFE ATT ORNEY Get. 4, 1949.

JAFFE PIEZOELECTRIC CRYSTAL ELEMENT 2 Sheets-Sheet 2 Filed Feb. 16, 1948MON IUM DIHYDROGEN ARSENATE Z852 WEB:

AMMONIUM DIHYDROGEN PHOSPHATE 0 IN DEGREES INVENTOR.

, HANS JAFFE FIG. 3

Zia fif ATT RNEY atented Oct. 4, 1949 2,483,641 PIEZOELECTRIC CRYSTALELEMENT Hans Jaffe, Cleveland, Ohio, assignor to The Brush DevelopmentCompany, Cleveland, Ohio,

a corporation of Ohio Application February 16, 1948, Serial No. 8,678

4 Claims. (Cl. 171-327) This invention pertains to a piezoelectriccrysal element cut with particular orientation from my one of a numberof representatives of a famly of crystals.

This application is :opending application a. continuation-in-part of afiled June 8, 1944, in the lame of Hans Jafie, Serial Number 539,312,now. ?atent No. 2,463,109, for Piezoelectric crystal neans and method ofusing same, and assigned the same assignee as the present application.

In the piezoelectric art useful applications have oen found for crystalsoffering several distinct types of relationship between a mechanicalstrain and a dielectric polarization or electric field. One well-knowntype is the 45 degree X-cut plate of Rochelle salt. also known as anexpander plate. In this crystal plate the mechanical strain is in adirection at right angles to the direction of the electric field. Such arelationship in a highly useful amount is also exhibited by the 45degree Z-cuts of P-type crystals, described and claimed in Patent No.2,463,109. Another type of useful relationship between strain andpolarization is that between a polarization and an expansion straincomponent parallel to this polarization. A crystal plate having such arelationship for a polarization in its thickness direction is known as athickness expander plate, such as the X-cut plate of quartz.

It has been shown in U. S. Patent 2,170,318 issued to W. G. Cady thatthickness expander plates can also be obtained from crystals of R0-chelle salt, and other crystals of the same or related symmetry, bycutting plates at angles substantially different from zero to theirthree axes X, Y, Z, the latter being orthogonal axes defined for thevarious crystals by accepted rules. These thickness expander plates areuseful in severalapplieations such as, for instance, the production orthe detection of compressional waves, in particular such waves inliquids, and for the maintenance of resonant vibrations of comparativelyhigh frequency in oscillating circuits.

The present invention pertains to thickness expander plates of theP-type group of crystals which are superior to such thickness expanderplates cut from Rochelle salt due to their ability to withstandtemperatures as high as about 120 degrees centigrade compared to 55degrees centigrade for Rochelle salt, and the smaller temperaturedependence of their dielectric and piezoelectric coeflicients. Theirability to withstand higher temperatures than Rochelle salt enables 2them to deliver higher levels or power when used as a transmitter ofultrasonic waves.

In accordance with this invention there is provided a plate-likethickness expander piezoelectric crystal element cut from a P-typecrystal. The plate has its thickness direction in a directionsubstantially parallel to a. symmetry plane of the crystal and inclinedat an angle greater than zero degrees and less than ninety degrees fromthe Z-aXiS of the P-type crystal.

The term P-type crystal is to .be understood as comprising primaryammonium phosphate (NI-IrHzPOr), primary potassium phosphate, primaryrubidium phosphate, the primary arsenates of ammonium, potassium andrubidium, isomorphous mixtures of any of these named compounds, and allother piezoelectrically active crystalline materials isomorphoustherewith. All of these crystals belong to the crystallographic symmetryclass Va, also known as the di-tetra 'onal alternating crystal class,and as the tetragonal sphenoidal class. It is characterized by thepresence of three two-fold axes of symmetry perpendicular to each otherand two planes of symmetry at right angles to each other andintersecting in one of the two-fold axes. The planes cut the othertwotwo-fold axes at angles of 45 degrees. This combination of symmetryelements makes that axis which is parallel to the two planes. ofsymmetry a four-fold alternating symmetry axis which is also the opticaxis of the crystal.

For the symmetry class of the P-type crystals there exist, according togeneral principles of piezoelectricity, two separate and independentpiezoelectric actions. One of these actions is that due to an electricfield or field component parallel to the optic axis. If a coordinatesystem X, Y, Z is used which has its Z-axis parallel to the optic axisof the crystal and the X and Y axes parallel to the two-fold axes ofsymmetry respectively, then this piezoelectric action appears as aninteraction be-tween an electric field parallel to the Z-axis and ashearing deformation about the Z- axis. With such a choice ofcoordinates the piezoelectric coefficients describing this interactionare characterized by the subscript 36.

Of the several P-type crystals, primary ammonium phosphate (NH4I-I2PO4)has been found to be of particular merit, and a certain cut thereof isclaimed in Patent No. 2,463,109. For the family of cuts herein claimed,primary ammonium phosphate and primary ammonium arsenate are ofparticular merit. Both of these crystals are stable up to at leastdegrees centigrade. They contain no water of crystallization so thatthey may be subjected to a vacuum for long periods of time withoutdetrimental effects. A further advantage of using an element cut from acrystal of the P-type is that when it is used in an enclosed transducerhousing, an amount of an extreme drying agent such as phosphorouspentoxide may be added to prevent moisture from establishing shuntcircuits across the element faces between the electrodes. Previously,when silica gel or the like was put into a transducer housing containinga Rochelle salt element, care had to be exercised to see that the silicagel was only partially dry, as completely dehydrated silica gel wouldrob the Rochelle salt of its water of crystallization, thereby renderingthe unit inoperative. Another important advantage gained by using anelement of the P-type instead of using a Rochelle salt element is thatthe P-type element may be coated with a thermo-setting material such asa phenolic condensate product (Bakelite), methyl methacrylate, or anyother material which will form a moisture-resistant coating upon beingheated over a period of time at a temperature of 120 degrees centigrade,or less. A further distinct advantage is realized when airixing anelement of primary ammonium phosphate to a base, such for example as aglass base, as a thermo-setting elastomer may be utilized since theelement will withstand the heat necessary for vulcanization.

It is an object of the invention to provide a suitably oriented plate ofsynthetic piezoelectric crystalline material which has no water ofcrystallization and which has sufiiciently high'piezoelectric activitythat the plate is highly useful in a piezoelectric transducer device.

A further object of the invention is to provide a suitably orientedplate of synthetic piezoelectric crystalline material useful in theproduction or the detection of compressional waves, particularly in thehigh frequency range, which is not severely limited in its use bytemperature conditions, and which will handle large amounts of powercompared to Rochelle salt plates.

It is also an object of the invention to provide a suitably orientedplate of synthetic piezoelectric crystalline material for maintainingresonant high frequency vibrations in oscillating circuits.

For a better understanding of the present invention, together with otherand further objects thereof, reference is had to the followingdescription taken in connection with the accompanying drawings, and itsscope will be pointed out in the appended claims.

In the two sheets of drawing Fig. 1 is a schematic isometric view of aP-type crystal showing two crystal elements cut in accordance with apreferred orientation; Fig. 2 is a. schematic view showing a family ofplates cut in accordance with the invention; and Fig. 3 is a graphshowing the voltage output of the family of plates shown in Fig. 2 as afunction of the angle of their cut.

The orientation of a plate-like piezoelectric crystal element withrespect to the orthogonal axes of the crystalline material from which itis out depends upon the characteristics which are desired. A plate maybe cut from a P-type crystal with such orientation that its thicknessdirection lies in one of the symmetry planes of the crystal and is at anangle to the Z axis of the crystalline material. If the highest possibleelectric charge is to be produced in the plate by a given pressureapplied to the plate, the angle should be chosen so that thepiezoelectric modulus d'a: is at its maximum. This modulus d'ndetermines the piezoelectric charge produced on a crystal per unitapplied compressional stress in the thickness direction. The value ofthe piezoelectric modulus d'as for an inclined plate of a P-type crystalhaving its thickness direction in a symmetry plane is given by theformula:

where 0 is the angle between the thickness direction of the plate andthe direction of the Z-axis. In many applications, however, this modulusis not a true measure of the piezoelectric usefulness of a crystal. Forinstance, when operating as a microphone acting at high frequencies,such as one megacycle or more, at which thickness expander plates areparticularly useful, the most important piezoelectric magnitude is theopencircuit voltage output per unit applied stress. In a plate whosethickness direction is perpendicular to a symmetry axis of a P-typecrystal this voltage output is given by a piezoelectric coefficienttermed the elasto-electric coeificient and designated by the letter 9 inPatent No. 2,463,109. The rules for transforming this coeihcient g toinclined axes are the same as for the transforma tion of the modulus d.It would therefore appear that the value 0=55 would give the preferredplate in respect to voltage output. This is not so, however, as thecoeflicient g is not the true measure of the voltage output in case ofplates whose thickness direction is inclined to the Z-axis of a P-typecrystal. A more accurate measure of this voltage output is given bywhere K is the effective dielectric constant of the inclined plate. Thisratio for inclined plates is not identical with the g coeflicient. Thereason for the difference is found in the fact that the electric fieldand dielectric polarization in these inclined plates are not parallel toeach other. The effective dielectric constant (that is the capacitycompared to an air condenser of the same dimensions) of a plate with itsthickness direction inclined by an angle 0 to the Z-axis of a P-typecrystal is given by the relation:

where K: and Kx are, respectively, the dielectric constants for the Zand X directions.

In this relation the clamped values for the dielectric constants shouldbe used because in typical applications of these thickness expanderplates the crystal is prevented from lateral motions.

The voltage output is thus given by the efiective voltage outputcoefficient The piezoelectric moduli are d14=1.5 and dac=+48.0, the unitbeing 10- coulomb/newton.

For the crystal primary ammonium arsenate, the clamped dielectricconstants are Kz=14.0 and lie-=75, giving a ratio of 5.36. Further Ihave found dl4=+41 and d;|e=-l-31-10-- coulomb/newton.

In Fig. 1 there is shown a bar it of P-type crystalline material withits X, Y and Z orthogonal axes indicated. The bar It is obtained from asynthetically grown crystal (not shown in its entirety) by cutting theedges of the bar at 45 degrees to the natural prism faces of thecrystal. The pyramidal and cap ll of the grown crystal may be used toorient the crystal bar during cutting. Plate is obtained by slicing thebar In at an angle of 45 degrees to one of the edges, and plate I3 isobtained by slicing the bar at an angle of 45 degrees to another of theedges. The thickness direction of both of the plates is at an angle of45 degrees to the Z axis, and the two plates are equivalent to eachother.

Fig. 2 shows schematically a P-type crystal IS with its mutuallyperpendicular symmetry planes l6, l1 intersecting in the Z axis. Afamily of thickness expander plates 18 to 24 is indicated with the anglevarying from greater than zero degrees to less than ninety degrees. Thecrystal plate 24 is shown with an electrode 25 on one of its majorfaces. It is to be understood that its other major face is to beelectroded, and it is to be further understood that each of the otherplates l2, l3 and l8-23 may be similarly electroded.

In Fig. 3 there is shown in curve form the voltage output versus angle0. It is seen that the maximum voltage output is obtained at an angle 0of about 42 degrees for ammonium dihydrogen phosphate and 40 degrees forammonium dihydrogen arsenate. The curves are rather flat in the vicinityof the maximum, permitting to choose an angle 0 several degrees awayfrom the theoretical optimum without noticeable loss in output. In theparticular case of ammonium dihydrogen phosphate, the output for theangle 0=45 is extremely close to the maximum theoretical output. Thepractical convenience of cutting plates at an angle of 45 degrees to theZ-axis compared to cutting at an odd angle, such as 42 degrees, has ledto the preference of the value 0:45 for this crystal.

The angle 0 giving maximum voltage output depends only on the ratio ofthe dielectric constants Kx and K1 and satisfies the equation:

The specified angles of orientation 0 lie between zero and degrees. Itmay be noted that the equation given to derive the value of 6 for maximum voltage output will lead to two values which are supplementary inrespect to degrees. The two angles so obtained are identical in terms ofcrystal symmetry.

While there have been described what are at present considered to be thepreferred embodiments of this invention, it will be obvious to thoseskilled in the art that various changes and modifications may be madetherein without departing from the invention, and it is, therefore,aimed in the appended claims to cover all such changes and modificationsas fall within the true spirit and scope of the invention.

I claim:

1. A plate-like thickness expander piezoelectric crystal element cutfrom an arsenate P-type crystal, said plate having its thicknessdirection in a direction substantially parallel to a symmetry plane ofsaid crystal and inclined at an anglegreater than zero degrees and lessthan ninety degrees from the Z-axis of said P-type crystal.

2. A plate-like thickness expander piezoelectric crystal element cutfrom a P-type crystal, said plate having its thickness direction in adirection substantially parallel to a symmetry plane of said crystal andinclined to the Z-axis by an angle 0 satisfying the equation whereby thevoltage output for compression in the thickness direction issubstantially a maximum.

3. A plate-like thickness expander piezoelectric crystal element cutfrom a P-type crystal as set forth in claim 2, in which said crystal isa primary ammonium phosphate crystal, and said angle of inclination issubstantially 45 degrees.

4. A plate-like thickness expander crystal element cut from a P-typecrystal as set forth in claim 2, in which said crystal is a primaryammonium arsenate crystal, and said angle of inclination issubstantially 40 degrees.

HANS JAFFE.

No references cited.

